Notre Dame Journal of Formal Logic

Model Companions of $T_{\rm Aut}$ for Stable T

John T. Baldwin and Saharon Shelah


We introduce the notion T does not omit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property (nfcp). For any theory T, form a new theory $T_{\rm Aut}$ by adding a new unary function symbol and axioms asserting it is an automorphism. The main result of the paper asserts the following: If T is a stable theory, T does not admit obstructions if and only if $T_{\rm Aut}$ has a model companion. The proof involves some interesting new consequences of the nfcp.

Article information

Notre Dame J. Formal Logic Volume 42, Number 3 (2001), 129-142.

First available: 12 September 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C45: Classification theory, stability and related concepts [See also 03C48]

stability expansion by automorphism


Baldwin, John T.; Shelah, Saharon. Model Companions of $T_{\rm Aut}$ for Stable T . Notre Dame Journal of Formal Logic 42 (2001), no. 3, 129--142. doi:10.1305/ndjfl/1063372196.

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